GlenCalc

Earth curvature calculator

From a height, your line of sight touches the Earth at the horizon. Beyond it, the lower part of a distant object is hidden.

Your answer

Hidden height32.68 ft
Distance to the horizon3 mi
Drop below a level line at that distanceSeen from the surface, eye height zero66.69 ft

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How we worked it out

Updated as you change the numbers.

  1. Horizon distance = √(2Rh + h²), with R = 6,371 km.
  2. Hidden height = √((d − horizon)² + R²) − R.
  3. Refraction is modeled by a larger effective radius, R ÷ (1 − 0.13).

Method and assumptions

A sphere of mean radius 6,371 km. Refraction varies with weather, especially over water, so real views are often a little better than pure geometry.

Questions

How much of an object 10 miles away is hidden from 6 feet up?

About 32.7 feet, with no refraction. The horizon is 3.0 miles away.

Sources

Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.

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